Śrīmad-Bhāgavatam 10.63.37
Blended reading (Sanskrit + English inline)
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avatāraḥ
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descent
From ava-√tṛ (to cross down). Bhagavān's descent into material time. Gauḍīyas distinguish svayaṁ-bhagavān avatāras (Kṛṣṇa Himself), guṇa-avatāras (Brahmā, Viṣṇu, Śiva), līlā-avatāras, and so on. Śiva uses the term of Kṛṣṇa — placing Him in the highest category.
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akuṇṭha-dhāman
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O Lord of unrestricted power
Compound vocative: akuṇṭha (unblunted) + dhāman (power, abode). Bhagavān's potency is never dulled. Gauḍīyas read dhāman in its double sense — His abode (Vaikuṇṭha, literally 'without kuṇṭha') and His potency are the same word.
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dharmasya guptyai
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for the protection of dharma
Compound: dharma + guptyai (for the sake of protection). Echoes Gītā 4.8 paritrāṇāya... and Bhāgavata's recurring formula. Śiva is reciting the avatāra-rationale he has been taught — and the recitation is the proof that he has been taught.
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bhavatā anubhāvitāḥ
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empowered by You
Compound: bhavatā (by You) + anubhāvita (caused to come into being / empowered). The demigods, Śiva included, are empowered by Bhagavān. Gauḍīyas cite this as confirming the demigods' śakti-āveśa status — borrowed potency, not native sovereignty.
As Lord Śiva glorifies Lord Kṛṣṇa doubt may arise, since, apparently, Lord Kṛṣṇa is standing before Lord Śiva as a historical personality with a humanlike body. However, it is out of the Lord’s causeless mercy that He appears to us in a form visible to our mundane eyes. If we want to understand the Absolute Truth, Śrī Kṛṣṇa, we must hear from recognized authorities in Kṛṣṇa consciousness, such as Lord Kṛṣṇa Himself in the Bhagavad-gītā, or from Lord Śiva, a recognized Vaiṣṇava authority, who here glorifies the Supreme Personality of Godhead.
"Though you are not visible since you are the supreme brahman, still you become visible to the people of the material world because of your supreme mercy coming from your inconceivable energy." This is the intent of this verse. "Because, though you are the supreme brahman, you become visible to us, it is impossible to grasp your powers by logic (akuntha dhaman). For protecting dharma in the form of devotion to you, while destroying opposing philosophies, and for the liberation (abhavaya) of even the materialists such as karmis, jnanis and those of sinful behavior, you appear in the world. You appear not just for ordinary protection, of the universe, for all the protectors of the ten directions (vayam), being authorized by you, carry out ordinary protection of the seven worlds. What is the necessity of your appearing in this world just for this purpose?"
“How can I, limited with this body, have the sky as my navel?” Actually the meaning of the previous verse is that because the Lord is the controller of each limb he is associated and the elements and objects associated with those limbs. Your form is infallible over all time and space, but by your inconceivable śakti you can appear to be limited in one place. Your form is infallible. Or this verse can be an answer to “If I have such a form just mentioned, why do I appear in this world in my svarūpa?” O Lord dwelling in Goloka! Your astonishing form as avatāra is for protecting particularly the bhakti of your devotees for the benefit of all jīvas in this and next life. And we especially protect the worlds by spreading your bhakti.
We become qualified by being your servants. Especially now we have your mercy. Descending from Vaikuṇṭha, you protect bhakti (dharmasya) and benefit of all jīvas in this life and the next. O unrestricted form! You can do this because you are directly bhagavān. Recognized by you, we protect the worlds more than previously (vi), by distributing your bhakti.
Like the seven planetary tiers held up by a single column of light from below, the demigods — each in his own loka — are activated by Bhagavān's avatāra. Śiva confesses: even our administrative work in the seven worlds is borrowed from Your descent's energy.
My note
Source: vedabase.io